Write the equation of the quadratic function whose graph is a parabola containing the points (10,72), (0,−3), and (−5,34.5).

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izboknil3 · Accepted Answer

Given: Given points are (10,72), (0,−3), (−5,34.5) We want to find the equation of parabola passing through the given points. Calculation: The general equation of the parabola is y=ax2+bx+c Parabola passes through the given points are (10,72), (0,−3), (−5,34.5).Therefore points satisfies equation of the parabola. Therefore (10,72)⇒72=a(10)2+b(10)+c (0.–3)⇒−3=a(0)2+b(0)+c (−5,34.5)⇒34.5=a(−5)2+b(−5)+c Therefore we get system of equations {=100a+10b+c=72.......1c=−3.......225a–5b+c=34.5.......3 By solving above system of equation Substituting C=−3 in equation 1 and 3 we get 100a+10b–3=72 ⇒100a=72+3–10b ⇒a=75−10b20 ⇒a=15−2b20 Substituting a=15−2b20 and c=−3 in equation 3 we get 25a–5b+c=34.5 ⇒25(15−2b20)−5b–3=34.5 ⇒75−10b4−5b=37.5 ⇒75−10b–20b=150 ⇒75–30b=150 ⇒30b=75–150 ⇒30b=75 ⇒b=−7530 ⇒b=−52 Therefore a=15−2b20 =15−2(−52)20 =15+520 =2020 a=1 ⇒a=1 Therefore we get

Write the equation of the quadratic function whose graph is a parabola containin

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